Manual Geomag

8/12/2019 Manual Geomag

1/18

1

GeoMag

USING GEOMAG 2

UTM COORDINATE SYSTEM 4

GEODETIC DATUMS AND ELLIPSOIDS 11

A BRIEF INTRODUCTION TO GEOMAGNETISM 14

EARTH MAGNETIC FIELD MAPS 16

ABOUT GEOMAG 18


2/18

2

Using GeoMag

GeoMag is a very simple program to use. Data items can be directly typed into any of the

white fields, except the Datum and Continents. These items must be selected from a fixednumber of predefined choices in drop down lists. For each of the data fields, the up/downarrow on their sides will increment or decrement the value in the field. Whenever a dataitem changes, the dependent fields will change according to the parameters of theconversion. For example, changing a Longitude will change the X/Y UTM coordinates andzone, based on the new Longitude and the old Latitude. The UTM Convergence, MagneticDeclination and the Bearing Compass will always be updated for changes in position andtime.


3/18

3

Below are the valid ranges for each data field.

Data Item RangeDate 1900.00 to 2004.99

Elevation 0.0 to 599.99 kilometers

Longitude 0.0 to 179 degrees, 59.99 minutes

Latitude 0.0 to 89 degrees, 59.99 minutes

UTM Easting 160 to 800 kilometers, 999.99 meters,

depends on Y/Latitude

UTM Northing 0.0 to 9999 kilometers, 999.99 meters

UTM Zone 1 to 60 for the northern hemisphere,

-1 to -60 for the southern hemisphere


4/18

4

UTM Coordinate System

The UTM (Universal Transverse Mercator) grid was devised as one way of solving thecartographer's dilemma: how to represent the (nearly) spherical earth's surface on a fiatsheet of paper. Latitude and longitude coordinates are sufficient when long distances areto be covered. (Pilots and sailors use them almost exclusively.) However, for ground teamswho cover only a few miles, latitude-longitude is much too cumbersome to be practical. Forexample, subdividing tic-marks for latitude-longitude are shown only in two places alongthe edge of a 7-1/2 minute quad map. Furthermore, the subdivisions of the units (minutesand seconds) are one-sixtieth of the larger unit. We are not accustomed to dividing lengthsby sixtieths, as were the Babylonians who invented this system 4000 years ago. Anotherlimitation is that a unit of longitude, a degree, represents less distance as one moves awayfrom the equator. This complicates matters when one needs to calculate the distance or

bearing from one point to another.Spherical trigonometry or other complex mathematical methods must be used to makethese calculations. These are not impossible of course, just inconvenient.

The UTM system was developed with guidelines that it would: (1) be a square grid; (2)have no negative numbers in the coordinates; (3) read left-to-right and bottom-to-top and(4) be decimal - based.

To accomplish these goals, the UTM system divides the earth's sphere into 60 zones;each is six degrees of longitude wide. The zones are numbered I through 60, west-to-east,beginning at 180 degrees west longitude. Figure 1 shows the zone numbering system ona continental outline map. Although not shown on this map, the zones cover only the area

between 80 degrees south and 84 degrees north latitudes. Different grids (not describedhere) cover the polar areas.


5/18

5

Figure 1 : The numbering system for UTM zones. The zones extend from 80 degreessouth to 84 degrees north latitudes.

The metric system is used as the units of the UTM coordinates. It may be convenient toremember (as a possible trivia answer) that the distance from the equator to either pole is10,000,000 meters or 10,000 kilometers. To be exact, a kilometer is equal to nearly 0.625of a mile or 0.62137 miles.

A square grid is superimposed on each zone and aligned so its vertical lines are parallel tothe center of the zone. This centerline is called the central meridian, and is three degreesof longitude from each zone boundary.

The UTM coordinates (measures of distance) are arranged so they always read from left-to-right and from bottom-to-top. This is done as follows. In the Northern Hemisphere theorigin, or zero point, of the horizontal lines is at the equator, while in the SouthernHemisphere the origin is at the South Pole.Establishing coordinates for the vertical lines was done differently. The vertical line at thecenter of each zone (central meridian) was arbitrarily assigned the value of 500 km toavoid having negative coordinate values. Assigning the value of 500 km to the center ofeach zone causes the zero point to fall in another zone - the one to its left (west). For thisreason, you will never see a zero value for an east-west coordinate. The smallest value is160 km and it is at the equator. As one moves away from the equator, the UTM eastcoordinate at the zone's western edge has larger and larger values. At 84 degrees northlatitude it is 465 km. Likewise, the eastern (right) zone boundaries will have coordinates of834 km at the equator and 515 km at 84 degrees north latitude. The way the square grid isplaced on each zone is shown in Figure 2 . Note that this drawing is not to scale; thehorizontal axis is highly exaggerated.


6/18

6

Figure 2 : The square UTM grid that is superimposed on each zone. This drawing is not toscale.

Figure 3 shows a portion of zones 10 and 11 in the western U.S. Nevada, quiteaccidentally, lies totally in zone 11, while California falls in both zones 10 and 11. Thelatitude-longitude and UTM coordinates are both shown in this figure to illustrate theirrelationship. Note that the UTM lines at zone boundaries meet at slight angles, and thewidth (number of kilometers) of the zones is greater near the bottom (south) than at the top

in this illustration. Observe also the square UTM grid is parallel to the central meridian.

Figure 3 : UTM zones 10 and 11 in California and Nevada.


7/18


8/18

8

Figure 5 : A corner of a 7 .5 minute USCS topographic map showing UTM coordinates

As taught in the U.S. Army, it should be noted that some teams learn UTM coordinates asa six-digit number. This number is created using the two large, bold-type UTM numbersfrom the map and the tenths from dividing the space between the grid lines. The decimalpoint is omitted. In addition, they learn to "read right up"; thus, presenting the number inthe correct format. Therefore, the coordinates mentioned above would be transmitted as052-961.

The UTM zone number will be found in the information printed on the lower left-handcorner of the map.

If you are plotting bearings very accurately, as you would during radiolocation of an ELT,one additional factor should be considered.

The only place where the UTM grid is aligned exactly true north is at the midpoint of azone (at the central meridian). The grid will be rotated slightly counterclockwise forlocations west (left) of the central meridian. This can be seen in Figure 4. Note how theUTM grid is not quite parallel to the edges of the map. Similarly, it will have a smallclockwise rotation east of the central meridian. The amount of rotation increases as youmove away from the central meridian and is maximized at the zone boundaries. Thisdifference between true north and UTM grid north is called the convergence, so namedbecause the meridians converge as they approach the poles. In the continental U.S. theconvergence will never exceed 2.5 degrees. If you need to know the convergence, it isshown on a diagram on the map in Figure 6. The vertical line with the star at its endrepresents true north, while the line with the notation GN (abbreviation for grid north) at its

end shows the angle (not to scale) of the UTM grid. The convergence for this map isshown as 0 degrees, 57 minutes, which is the same as 57 divided by 60 or about 1.0degrees. On this map grid north is counterclockwise from true north by 1.0 degrees.

Figure 6 also shows the relation between true north and magnetic north. Note the legendbelow the figure gives a year that is associated with the magnetic declination. That'sbecause declination is not a constant value - it changes with time. The change is slow; onedegree every 10 years is common in parts of the U.S. But if you're using a 30-year-oldmap, the declination printed on it may be wrong by three degrees. On this map, thedifference between magnetic north (in 1984) and UTM grid north is 21.0 degrees minus 1.0


9/18

9

degrees, or 20.0 degrees. Knowing the exact values of convergence and declination is notimportant unless you are doing precise navigation or making extremely accurate plots ofbearings.

Figure 6 : Diagram on USGS topographic maps that shows the angular relations amonggrid north, true north and magnetic north.

One further advantage the UTM system offers is its coordinates can be convened tolatitude-longitude and vice versa. The mathematical equations for doing this are verycomplicated, but are easily handled by computers, including small hand held ones. Beingable to make these conversions is quite useful when coordinating search operationsinvolving both ground teams and air resources. If a ground team requests a victimevacuation by helicopter and gives its location in UTM coordinates, these can beconverted to latitude-longitude. The aircraft crew can then use its on-board navigationequipment to locate the pickup site. Another use of the conversion process is in theplotting of locations on a map. In searches for missing aircraft, the FAA is sometimes ableto furnish a record of the aircraft's flight path from its radar records (NTAP). Theselocations are always given in latitude-longitude coordinates. Plotting these on a map canbe very time-consuming. But, if they are converted to UTM coordinates, then they can beplotted very quickly.

These are the features of the UTM coordinate system that you need to use in the field. Itprovides a rapid, simple and accurate way to report your location. All that remains to bedone is adding the UTM grid lines to your maps. Use a long straightedge to connect theblue tic-marks with a pencil or fine-point pen. This would be a good project for a cold winternight or at a team meeting when discussing map reading. Then, on your next mission, theUTM grid will be waiting for you to use it.


10/18

10

For those interested in more details about the UTM system the following references arerecommended:

Maps for America , by Morris M. Thompson, published by the United States GeologicalSurvey, 1979. This is an excellent reference book that describes all the features on USGSmaps. The appendix has a thorough description of the UTM coordinate system.

United States Army Technical Manuals TM 5-241-1, "Grids and Grid References", and TM5-241-8, "Universal Transverse Mercator Grid". The first of these describes the way theUTM system forms the basis for the Military Grid Reference System. The latter providesthe mathematical equations for converting UTM coordinates to latitude - longitude and viceversa.


11/18

11

Geodetic Datums and Ellipsoids

Hundreds of geodetic datums are in use around the world. The Global Positioning systemis based on the World Geodetic System 1984 (WGS-84). The Defense Mapping Agencypublishes parameters for simple XYZ conversion between many datums and WGS-84.Coordinate values resulting from interpreting latitude, longitude, and height values basedon one datum as though they were based in another datum can cause position errors inthree dimensions of up to one kilometer.

Datum conversions are accomplished by various methods. Complete datum conversion isbased on seven parameter transformations that include three translation parameters, threerotation parameters and a scale parameter. Simple three parameter conversion betweenlatitude, longitude, and height in different datums can be accomplished by conversion

through Earth-Centered, Earth Fixed XYZ Cartesian coordinates in one reference datumand three origin offsets that approximate differences in rotation, translation and scale.GeoMag uses the Standard Molodensky formulas to convert latitude, longitude, andellipsoid height in one datum to another datum.

Datums and their Parameters Available with GeoMag

Datum Ellipsoid DX DY DZ Adindan Clarke 1880 -162.0 -12.0 206.0 Arc 1950 Clarke 1880 -143.0 -90.0 -294.0 Arc 1960 Clarke 1880 -160.0 -8.0 -300.0

Australian 1966 Australian National -133.0 -48.0 148.0 Australian 1984 Australian National -134.0 -48.0 149.0Camp Area Astro International 1909 -104.0 -129.0 230.0Cape Clarke 1880 -136.0 -108.0 -292.0European 1950 International 1909 -87.0 -98.0 -121.0European 1979 International 1967 -86.0 -98.0 -119.0Geodetic 1949 International 1967 84.0 -22.0 209.0Hong Kong 1963 International 1967 -156.0 -271.0 -189.0Hu Tzu Shan International 1967 -634.0 -549.0 -201.0Indian Everest 289.0 734.0 257.0North American 1927 Clarke 1866 -8.0 160.0 176.0North American 1983 GRS 80 0.0 0.0 0.0Oman Clarke 1880 -346.0 -1.0 224.0Ordnance Survey 1936 Airy 375.0 -111.0 431.0Pulkovo 1942 Krassovsky 1942 27.0 -135.0 -89.0South American 1956 International 1967 -288.0 175.0 -376.0South American 1969 South American 1969 -57.0 1.0 -41.0Tokyo Bessel 1841 -128.0 481.0 664.0WGS 1972 WGS 72 0.0 0.0 -4.5WGS 1984 WGS 84 0.0 0.0 0.0


12/18

12

Early ideas of the figure of the Earth resulted in descriptions of the Earth as an oyster (TheBabylonians before 3000 BC), a rectangular box, a circular disk, a cylindrical column, aspherical ball, and a very round pear (Columbus in the last years of his life). Flat Earthmodels are still used for plane surveying, over distances short enough so that Earthcurvature is insignificant (less than 10 km).

Spherical Earth models represent the shape of the Earth with a sphere of a specifiedradius. Spherical Earth models are often used for short range navigation (VOR-DME) andfor global distance approximations. Spherical models fail to model the actual shape of theEarth. The slight flattening of the Earth at the poles results in about a twenty-kilometerdifference at the poles between an average spherical radius and the measured polarradius of the Earth.


13/18

13

Figure 1 : Ellipsoidal Parameters

Ellipsoidal Earth models are required for accurate range and bearing calculations over longdistances. Loran-C, and GPS navigation receivers use ellipsoidal Earth models to computeposition and waypoint information. Ellipsoidal models define an ellipsoid with an equatorialradius and a polar radius. The best of these models can represent the shape of the Earthover the smoothed, averaged sea-surface to within about one hundred meters.

Ellipsoids and their Parameters Available with GeoMag

Ellipsoid Semi-Major Axis Semi-Minor Axis 1/fClarke 1866 6378206.4 6356583.8 294.979Clarke 1880 6378249.145 6356514.86955 293.465

Australian National 6378160.0 6356774.719 298.240International 1909 6378388.0 6356911.94613 297.000International 1967 6378157.5 6356772.2 298.250Everest 6377276.3452 6356075.4133 300.802GRS 80 6378137.0 6356752.31414 298.257

Airy 6377563.396 6356256.91 299.325Krassovsky 1942 6378245.0 6356863.0188 298.300South American 1969 6378160.0 6356774.7192 298.250Bessel 1841 6377397.155 6356078.96284 299.153WGS 72 6378135.0 6356750.519915 298.260WGS 84 6378137.0 6356752.31414 298.257


14/18

14

A Brief Introduction to Geomagnetism

The following is intended to give those users unfamiliar with Earth magnetism anintroduction to the various parameters calculated by the GeoMag program and anunderstanding of the changing nature of the Earths magnetic field. If you are interested inpursuing the subject further, some references are listed at the end of this section.

Figure 1 : Earths Magnetic Field

The Earth's magnetic field resembles, in general; the field generated by a dipole magnet(i.e., a straight magnet with a north and South Pole) located at the center of the Earth. Theaxis of the dipole is offset from the axis of the Earth's rotation by approximately 11degrees. This means that the north and south geographic poles and the north and southmagnetic poles are not located in the same place. At any point, the magnetic field ischaracterized by a direction and intensity, which can be measured. The geomagnetic polesare located in the area where the lines of force are perpendicular to the Earth's surfaceand are sometimes referred to as the dip poles (dip = 90 degrees). The physical location ofthe magnetic pole is actually an area rather than a single point. Because of the changingnature of Earths magnetic field, the location of the magnetic poles also changes. Thecurrent locations of the magnetic poles are approximately:

North Pole: 78.5 N and 103.4 W degrees, near Ellef Ringnes Island, Canada

South Pole: 65 S and 139 W degrees, in Commonwealth Bay, Antarctica


15/18

15

Figure 2 : Magnetic Field Vector

The Earth's magnetic field is described by seven parameters. These are declination (D),

inclination (I), horizontal intensity (H), vertical intensity (Z), total intensity (F) and the north(X) and east (Y) components of the horizontal intensity. The parameter most frequentlyrequested and most often misunderstood is magnetic declination or variation (D). This isthe angle made between the trace of the total magnetic field in the horizontal plane (H) andtrue north. D is considered positive when the angle measured is east of true north andnegative when west. The inclination or dip, I, is the angle between the horizontal plane andthe total magnetic field. Inclination, also called magnetic dip, is considered positive whendownward pointing. These elements, D, I and H give a full vector representation of themagnetic field, F. Vertical intensity is the trace of the total intensity in the vertical plane andis considered positive when I is positive, that is downward pointing. The east component,Y, is considered positive when pointing east and the north component, X, is positive when

pointing towards geographic north. At any specific point, the values of the magnetic elements are changing. The changes arenot uniform over area or time. Some types of change are distinguishable. Three important,classifiable changes are the diurnal, secular and storm variations. The small regularfluctuations in the magnetic field that occur more or less regularly every 24 hours arecalled diurnal variations. Secular changes extend over years with generally smoothincreases or decreases in the field. Magnetic storms are sudden and potentially largedisturbances in the magnetic field, which may last hours or days. Of these changes, theleast understood is the long-term change that occurs over years in the main magnetic field.Mathematical models can approximate the magnetic field over short periods of time, butbecause the secular change is not predictable, the potential for error increases the furtherin time from the base epoch the calculations are. For this reason, it is important to use themost current accepted models of the magnetic field. These models are produced aboutevery 5 years and are available from NGDC and the World Data Centers.


16/18

16

Earth Magnetic Field Maps

Figure 1 : Migration of the Earth's North Pole over Time

Figure 1 shows how the Earth's magnetic north pole, located in far northern Canada, hasmoved over the past 50 years. The rate of change has been approximately one degree oflatitude every five years. This is why older maps do not have the correct, current magneticdeclination printed in their legends.


17/18

17

Figure 2 : Transverse Mercator Projection with Magnetic Color Contours

In Figure 2, the warmer colors, e.g. red and orange, represent increasing values of positivemagnetic declination. The cooler colors, e.g. green and blue, represent decreasing valuesof negative magnetic declination. Yellow represent near zero declination.


18/18

18

About GeoMag

GeoMag is a free ware program and is copyrighted. Distribute freely and enjoy

Garry Petrie is the author of GeoMag.He can be reached at:

19880 NW Nestucca DrivePortland, Oregon 97229

503-264-3027 day503-690-5465 evenings

[email protected]

Documents

Manual Geomag